In nitrogen monoxide, NO, the radical can be assigned to both the nitrogen and the oxygen, right? It would depend on what the question asks but if asked for the "most stable" would you put the radical on oxygen since it is more electronegative? Also, is this considered resonance (the radical being able to jump around)?

I think if you are looking for the most stable form of the molecule then you should put the radical on the oxygen since it is more electronegative. For most resonance structures we always used electronegativities to determine if the particular arrangement would be the most stable form.